3. For each set below, circle "YES" if it is a vector space, or circle "NO" if it is not a vector space. Whenever you circle "YES" you do not have to justify your answer. Whenever you circle "NO", give a counterexample/reason. (15 points) S = {a + bx + cx² E P2: abc = 0} a. YES NO Counterexample: bnd a eM3: a, b f 0] b. А — YES NO Counterexample: C. Let the vector space V be the set of real numbers, with addition and scalar multiplication defined by x + y = the maximum of x and y kx = kx (the usual scalar multiplication of R) YES NO Counterexample:
3. For each set below, circle "YES" if it is a vector space, or circle "NO" if it is not a vector space. Whenever you circle "YES" you do not have to justify your answer. Whenever you circle "NO", give a counterexample/reason. (15 points) S = {a + bx + cx² E P2: abc = 0} a. YES NO Counterexample: bnd a eM3: a, b f 0] b. А — YES NO Counterexample: C. Let the vector space V be the set of real numbers, with addition and scalar multiplication defined by x + y = the maximum of x and y kx = kx (the usual scalar multiplication of R) YES NO Counterexample:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A, b
Transcribed Image Text:3. For each set below, circle “YES" if it is a vector space, or circle "NO" if it is not a vector
space. Whenever you circle "YES" you do not have to justify your answer. Whenever
you circle "NO", give a counterexample/reason. (15 points)
S = {a + bx + cx² E P2: abc = 0}
a.
YES
NO
Counterexample:
hnd
a
b. A =
eM3: a, b
YES
NO
Counterexample:
C. Let the vector space V be the set of real numbers, with addition and scalar
multiplication defined by
x + y = the maximum of x and y
kx = kx (the usual scalar multiplication of R)
YES
NO
Counterexample:
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